The Unilateral Dynamic Characteristics of Three-Electrode Vacuum Tubes

Abstract

Unilateral dynamic characteristics of vacuum tube when plate circuit includes resistance, inductance or capacity.---(1) Theoretical equations. For the case of pure resistance ($R$), the Van der Bijl parabolic relation between plate current and effective grid voltage is expressed as a power series in $e$ sin pt, the impressed simple harmonic grid voltage. The coefficients of the various harmonics involve $R$, the $n$th harmonic reaching a maximum value when $R$ equals $\frac{(n\ensuremath{-}2)}{3}$ times R0 the tube resistance. For the fundamental the maximum energy output for a given plate battery is secured when $R=0.81 {R}_{0}$. The dynamic characteristic was obtained by compounding the harmonics into a single curve; it approaches a straight line as the resistance is increased. For the case of pure inductance, the plate current is expressed as a Fourier series. The dynamic characteristic is a closed loop whose area is proportional to the energy in the inductance. This loop reduces to an ellipse for small values of $e$, in which case the tube functions as an alternator whose internal impedance is a function of the external load. The insertion of a condenser instead of an equivalent inductance gives identical results except that the phase angle of the various harmonics is shifted. (2) Experimental verification. The effects on the plate current of varying the alternating grid voltage $e$, the static grid voltage ${E}_{c}$ and the plate voltage ${E}_{b}$, for a given value of resistance $R$ or inductance $l$, and the effect of varying $R$ or $l$ with constant ${E}_{b}$, ${E}_{c}$ and $e$ (15 or 20 volts), were determined and are shown in curves together with the corresponding theoretical values. A. W. E. 205B tube was used. The results show that the equations predict the harmonic constituents of the plate current as high as the fourth, for values of $e$ up to 15 or 20 volts (depending on ${E}_{b}$), the range for which the fundamental equation holds. For this range the coefficients of the various harmonics in the equation are proportional simply to ${e}^{n}$. The fundamental becomes greater while the other harmonics diminish as we approach the straight portion of the static characteristic and as we increase the plate potential.Circuit for producing pure sine wave electromotive force with frequency of 200,000 cycles.---The oscillating circuit and filters used are shown diagrammatically in Fig. 1.Pure resistance for high frequencies.---A platinized quartz fiber (diameter 0.01 mm.) with a resistance of 100 ohms per inch will carry 0.06 ampere when immersed in acidfree paraffin oil and has a negligible skin effect.